Learnable Filters for Geometric Scattering Modules

Area of Science:

• Machine Learning
• Graph Neural Networks
• Geometric Scattering

Background:

• Graph neural networks (GNNs) often struggle to capture long-range dependencies in graph data.
• Existing GNNs frequently rely on local neighborhood information (smoothness, similarity), limiting their relational learning capabilities.
• Geometric scattering transforms offer a principled way to extract features but lack adaptability.

Purpose of the Study:

• To introduce a novel, learnable module for GNNs inspired by geometric scattering transforms.
• To enhance GNNs' ability to learn longer-range graph relations.
• To develop a more parameter-efficient GNN architecture.

Main Methods:

• Proposed a learnable geometric scattering (LEGS) module based on relaxations of geometric scattering transforms.
• Integrated the LEGS module into GNN architectures, enabling adaptive tuning of graph wavelets.
• Evaluated LEGS-based networks on graph classification benchmarks and biochemical graph data exploration.

Main Results:

• LEGS-based GNNs demonstrated improved learning of longer-range graph relations compared to popular GNNs.
• The proposed module resulted in simplified architectures with significantly fewer learned parameters.
• LEGS networks matched or outperformed existing GNNs and handcrafted geometric scattering on various datasets, especially in biochemical domains.

Conclusions:

• The LEGS module offers a powerful and efficient approach to enhance GNNs for complex graph analysis.
• LEGS successfully integrates the benefits of geometric scattering with the adaptability of deep learning.
• This work advances GNN capabilities, particularly for applications in scientific domains like biochemistry.